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An open loop transfer function is given by G(s) = K (s + 1) / (s + 4)(s2 + 3s + 2). It has:
- a)One zero at infinity
- b)Three zeroes at infinity
- c)Two zeroes at infinity
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
An open loop transfer function is given by G(s) = K (s + 1) / (s + 4)(...
Explanation:
The given open loop transfer function is:
G(s) = K (s-1) / (s-4)(s^2-3s-2)
To find the number of zeroes at infinity, we need to determine the degree of the numerator and denominator polynomials.
Degree of the numerator polynomial:
The numerator polynomial is (s-1), which is a first-degree polynomial. Therefore, the degree of the numerator is 1.
Degree of the denominator polynomial:
The denominator polynomial is (s-4)(s^2-3s-2), which is a third-degree polynomial. Therefore, the degree of the denominator is 3.
To find the number of zeroes at infinity, we subtract the degree of the numerator from the degree of the denominator.
Number of zeroes at infinity = Degree of denominator - Degree of numerator
= 3 - 1
= 2
Conclusion:
The given open loop transfer function has two zeroes at infinity. Therefore, the correct answer is option 'C'.
The given open loop transfer function is:
G(s) = K (s-1) / (s-4)(s^2-3s-2)
To find the number of zeroes at infinity, we need to determine the degree of the numerator and denominator polynomials.
Degree of the numerator polynomial:
The numerator polynomial is (s-1), which is a first-degree polynomial. Therefore, the degree of the numerator is 1.
Degree of the denominator polynomial:
The denominator polynomial is (s-4)(s^2-3s-2), which is a third-degree polynomial. Therefore, the degree of the denominator is 3.
To find the number of zeroes at infinity, we subtract the degree of the numerator from the degree of the denominator.
Number of zeroes at infinity = Degree of denominator - Degree of numerator
= 3 - 1
= 2
Conclusion:
The given open loop transfer function has two zeroes at infinity. Therefore, the correct answer is option 'C'.
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Community Answer
An open loop transfer function is given by G(s) = K (s + 1) / (s + 4)(...
The formula to calculate a number of zeroes at infinity is P - Z. Here, P and Z are the number of poles and zeroes in a given transfer function.
We know that poles are calculated by equating the denominator to zero, and zeroes are calculated by equating the numerator to zero. So, for the above given transfer function, we get:
P = 3
Z = 1
So, the number of zeroes at infinity = 3 - 1 = 2
Hence, the correct answer is an option (c).
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